A casing bit, which may comprise a composite structure, for drilling a casing section into a subterranean formation, and which may include a portion configured to be drilled therethrough. Cutting elements and methods of use may be included. Adhesive, solder, electrically disbonding material, and braze affixation of a cutting element may be included. Differing abrasive material amount, characteristics, and size of cutting elements may be included. Telescoping casing sections and bits may be included. Embodiments may include: at least one gage section extending from the nose portion, at least one rotationally trailing groove formed in at least one of the plurality of blades, a movable blade, a leading face comprising superabrasive material, at least one of a drilling fluid nozzle and a sleeve, grooves for preferential failure, at least one rolling cone affixed to the nose portion, at least one sensor, discrete cutting element retention structures, and percussion inserts.

Claim:

What is claimed is:

1. A casing shoe configured for attachment to at least one section of casing and for drilling or reaming a wellbore as the at least one section of casing is advanced intocontact with subterranean formation material, the casing shoe comprising: a nose portion having an inner profile and an outer profile; a gage portion extending longitudinally from the nose portion; a plurality of blades; and a first plurality ofcutting elements fixedly mounted on the casing shoe in a first region of the casing shoe to be subsequently drilled through by another drilling tool, the first region extending radially from the longitudinal axis of the casing shoe to a first radialposition, each cutting element of the first plurality of cutting elements comprising a volume of abrasive material; a second plurality of cutting elements mounted on the casing shoe in a second region of the casing shoe not to be subsequently drilledthrough by another drilling tool, the second region extending radially outward from the first radial position to a second radial position, the second plurality of cutting elements having a material composition differing from the first plurality ofcutting elements, the first plurality of cutting elements being more susceptible to wear relative to the second plurality of cutting elements.

2. The casing shoe of claim 1, wherein at least one cutting element of the first plurality of cutting elements comprises a substrate attached to the volume of abrasive material, at least a portion of the substrate being substantially free ofcarbide.

3. The casing shoe of claim 2, wherein the entire substrate is substantially free of carbide.

4. The casing shoe of claim 2, wherein the at least a portion of the substrate comprises at least one material selected from a group consisting of steel, tungsten, bronze, brass, aluminum, molybdenum, an alloy of molybdenum, and a ceramic.

5. The casing shoe of claim 2, wherein at least a portion of a side surface of the volume of abrasive material is bonded to the substrate.

6. The casing shoe of claim 5, wherein the volume of abrasive material comprises at least one material selected from a group consisting of diamond, ceramic, boron nitride, impregnated material, hardfacing material, and carbide.

7. The casing shoe of claim 2, wherein the substrate comprises: a first region comprising a first material; and a second region comprising a second material having a composition different from a composition of the first material.

8. The casing shoe of claim 7, wherein the first region of the substrate comprises at least one material selected from a group consisting of steel, tungsten, bronze, brass, aluminum, molybdenum, an alloy of molybdenum, and a ceramic.

9. The casing shoe of claim 8, wherein the second region of the substrate comprises a cemented carbide material.

10. The casing shoe of claim 9, wherein the second region of the substrate is configured such that the second region of the substrate will be at least substantially removed from the at least one cutting element in response to drilling orreaming a wellbore with the casing shoe as the at least one section of casing is advanced into the wellbore.

12. The casing shoe of claim 11, wherein each cutting element of the second plurality of cutting elements comprises a polycrystalline diamond compact (PDC) cutting element.

13. The casing shoe of claim 1, wherein the cutting elements of the first plurality of cutting elements are confined such that the abrasive material of the first plurality of cutting elements will be at least substantially removed from thecasing shoe in response to drilling or reaming a wellbore with the casing shoe as the at least one section of casing is advanced into the wellbore and the casing shoe is used to drill or ream the wellbore.

14. A casing shoe configured for attachment to at least one section of casing and for drilling or reaming a wellbore as the at least one section of casing is advanced into contact with subterranean formation material, the casing shoecomprising: a nose portion having an inner profile and an outer profile; a gage portion extending longitudinally from the nose portion; a plurality of blades; and a first plurality of cutting elements mounted on the casing shoe in a first region ofthe casing shoe to be subsequently drilled through by another drilling tool, The first region extending radially from the longitudinal axis of the casing shoe to a first radial position, each cutting element of the first plurality of cutting elementscomprising a volume of abrasive material; a second plurality of cutting elements mounted on the casing shoe in a second region of the casing shoe not to be subsequently drilled through by another drilling tool, the second region extending radiallyoutward from the first radial position to a second radial position, the second plurality of cutting elements having a material composition differing from the first plurality of cutting elements, the first plurality of cutting elements being moresusceptible to wear relative to the second plurality of cutting elements; at least one cutting element of the first plurality of cutting elements comprises a substrate attached to the volume of abrasive material, at least a portion of the substratebeing substantially free of carbide; wherein the substrate comprises: a first region comprising a first material; and a second region comprising a second material having a composition different from a composition of the first material; each of thefirst region of the substrate and the second region of the substrate is bonded to a major planar surface of the volume of abrasive material on a side thereof opposite a cutting face of the at least one cutting element.

15. A casing shoe configured for attachment to at least one section of casing and for drilling or reaming a wellbore as the at least one section of casing is advanced into contact with subterranean formation material, the casing shoecomprising: a nose portion having an inner profile and an outer profile; a gage portion extending longitudinally from the nose portion; a plurality of blades; and a first plurality of cutting elements mounted on the casing shoe in a first region ofthe casing shoe to be subsequently drilled through by another drilling tool, The first region extending radially from the longitudinal axis of the casing shoe to a first radial position, each cutting element of the first plurality of cutting elementscomprising a volume of abrasive material; a second plurality of cutting elements mounted on the casing shoe in a second region of the casing shoe not to be subsequently drilled through by another drilling tool, the second region extending radiallyoutward from the first radial position to a second radial position, the second plurality of cutting elements having a material composition differing from the first plurality of cutting elements, the first plurality of cutting elements being moresusceptible to wear relative to the second plurality of cutting elements; the volume of abrasive material comprises polycrystalline diamond; each cutting element of the second plurality of cutting elements comprises a polycrystalline diamond compact(PDC) cutting element; an average quantity of abrasive material in the first plurality of cutting elements is less than an average quantity of abrasive material in the second plurality of cutting elements.

16. The casing shoe of claim 15, wherein the average size of the first plurality of cutting elements is less than the average size of the second plurality of cutting elements.

17. A method of designing a casing shoe for attachment to at least one section of casing and for drilling or reaming a wellbore as the at least one section of casing is advanced into the wellbore, the method comprising: identifying at least oneformation in which a wellbore is to be drilled or reamed by the casing shoe; designing a nose portion of the casing shoe having an inner profile, an outer profile, and a plurality of blades; selecting a first plurality of cutting elements to be fixedlymounted on the casing shoe in a first region of the casing shoe to be subsequently drilled through by another drilling tool, each cutting element of the first plurality of cutting elements comprising a volume of abrasive material, selecting the firstplurality of cutting elements comprising selecting the first plurality of cutting elements in consideration of the at least one formation in which a wellbore is to be drilled or reamed by the casing shoe such that the volumes of abrasive material of thefirst plurality of cutting elements will be at least substantially removed from the casing shoe as the wellbore is drilled or reamed by the casing shoe; and selecting a second plurality of cutting elements to be mounted on the casing shoe in a secondregion of the casing shoe not configured to be subsequently drilled through by another drilling tool, the second plurality of cutting elements differing from the first plurality of cutting elements.

18. A method of designing a casing shoe for attachment to at least one section of casing and for drilling or reaming a wellbore as the at least one section of casing is advanced into the wellbore, the method comprising: identifying at least oneformation in which a wellbore is to be drilled or reamed by the casing shoe; designing a nose portion of the casing shoe having an inner profile, an outer profile, and a plurality of blades; selecting a first plurality of cutting elements to be mountedon the casing shoe in a first region of the casing shoe to be subsequently drilled through by another drilling tool, each cutting element of the first plurality of cutting elements comprising a volume of abrasive material, selecting the first pluralityof cutting elements comprising selecting the first plurality of cutting elements in consideration of the at least one formation in which a wellbore is to be drilled or reamed by the casing shoe such that the volumes of abrasive material of the firstplurality of cutting elements will be at least substantially removed from the casing shoe as the wellbore is drilled or reamed by the casing shoe; and selecting a second plurality of cutting elements to be mounted on the casing shoe in a second regionof the casing shoe not configured to be subsequently drilled through by another drilling tool, the second plurality of cutting elements differing from the first plurality of cutting elements; selecting the volumes of abrasive material of the firstplurality of cutting elements to comprise polycrystalline diamond; selecting the second plurality of cutting elements to comprise polycrystalline diamond compact (PDC) cutting elements, an average quantity of polycrystalline diamond in the firstplurality of cutting elements being less than an average quantity of polycrystalline diamond in the second plurality of cutting elements.

19. The method of claim 18, further comprising selecting at least one cutting element of the first plurality of cutting elements to comprise a substrate attached to the volume of abrasive material, at least a portion of the substrate beingsubstantially free of carbide.

20. The method of claim 19, further comprising selecting the at least one element such that the substrate comprises: a first region comprising a first material; and a second region comprising a second material having a composition differentfrom a composition of the first material.

21. The method of claim 20, further comprising selecting the at least one element such that the first region of the substrate comprises at least one material selected from a group consisting of steel, tungsten, bronze, brass, aluminum,molybdenum, an alloy of molybdenum, and a ceramic, and such that the second region of the substrate comprises a cemented carbide material.